Indicators of transitions in biological systems

Flagged observation analyses as a tool for scoping and communication in integrated ecosystem assessments

Working groups for integrated ecosystem assessments are often challenged with understanding and assessing recent change in ecosystems. As a basis for this, the groups typically have at their disposal many time series and will often need to prioritize which ones to follow up for closer analyses and assessment. In this article we provide a procedure termed Flagged Observation analysis that can be applied to all the available time series to help identifying time series that should be prioritized. The statistical procedure first applies a structural time series model including a stochastic trend model to the data to estimate the long-term trend. The model adopts a state space representation, and the trend component is estimated by a Kalman filter algorithm. The algorithm obtains one- or more-years-ahead prediction values using all past information from the data. Thus, depending on the number of years the investigator wants to consider as "the most recent", the expected trend for these years is estimated through the statistical procedure by using only information from the years prior to them. Forecast bands are estimated around the predicted trends for the recent years, and in the final step, an assessment is made on the extent to which observations from the most recent years fall outside these forecast bands. Those that do, may be identified as flagged observations. A procedure is also presented for assessing whether the combined information from all the most recent observations form a pattern that deviates from the predicted trend and thus represents an unexpected tendency that may be flagged. In addition to form the basis for identifying time series that should be prioritized in an integrated ecosystem assessment, flagged observations can provide the basis for communicating with managers and stakeholders about recent ecosystem change. Applications of the framework are illustrated with two worked examples.

Early warning signals observed in motor activity preceding mood state change in bipolar disorder

INTRODUCTION

Alterations in motor activity are well-established symptoms of bipolar disorder, and time series of motor activity can be considered complex dynamical systems. In such systems, early warning signals (EWS) occur in a critical transition period preceding a sudden shift (tipping point) in the system. EWS are statistical observations occurring due to a system's declining ability to maintain homeostasis when approaching a tipping point. The aim was to identify critical transition periods preceding bipolar mood state changes.

METHODS

Participants with a validated bipolar diagnosis were included to a one-year follow-up study, with repeated assessments of the participants' mood. Motor activity was recorded continuously by a wrist-worn actigraph. Participants assessed to have relapsed during follow-up were analyzed. Recognized EWS features were extracted from the motor activity data and analyzed by an unsupervised change point detection algorithm, capable of processing multi-dimensional data and developed to identify when the statistical property of a time series changes.

RESULTS

Of 49 participants, four depressive and four hypomanic/manic relapses among six individuals occurred, recording actigraphy for 23.8 ± 0.2 h/day, for 39.8 ± 4.6 days. The algorithm detected change points in the time series and identified critical transition periods spanning 13.5 ± 7.2 days. For depressions 11.4 ± 1.8, and hypomania/mania 15.6 ± 10.2 days.

CONCLUSION

The change point detection algorithm seems capable of recognizing impending mood episodes in continuous flowing data streams. Hence, we present an innovative method for forecasting approaching relapses to improve the clinical management of bipolar disorder.

Early warning indicators capture catastrophic transitions driven by explicit rates of environmental change

In response to external changes, ecosystems can undergo catastrophic transitions. Early warning indicators aim to predict such transitions based on the phenomenon of critical slowing down at bifurcation points found under a constant environment. When an explicit rate of environmental change is considered, catastrophic transitions can become distinct phenomena from bifurcations, and result from a delayed response to noncatastrophic bifurcations. We use a trophic metacommunity model where transitions in time series and bifurcations of the system are distinct phenomena. We calculate early warning indicators from the time series of the continually changing system and show that they predict not the bifurcation of the underlying system but the actual catastrophic transition driven by the explicit rate of change. Predictions based on the bifurcation structure could miss catastrophic transitions that can still be captured by early warning signals calculated from time series. Our results expand the repertoire of mechanistic models used to anticipate catastrophic transitions to nonequilibrium ecological systems exposed to a constant rate of environmental change.

Application of early warning signs to physiological contexts: a comparison of multivariate indices in patients on long-term hemodialysis

Early warnings signs (EWSs) can anticipate abrupt changes in system state, known as "critical transitions," by detecting dynamic variations, including increases in variance, autocorrelation (AC), and cross-correlation. Numerous EWSs have been proposed; yet no consensus on which perform best exists. Here, we compared 15 multivariate EWSs in time series of 763 hemodialyzed patients, previously shown to present relevant critical transition dynamics. We calculated five EWSs based on AC, six on variance, one on cross-correlation, and three on AC and variance. We assessed their pairwise correlations, trends before death, and mortality predictive power, alone and in combination. Variance-based EWSs showed stronger correlations (r = 0.663 ± 0.222 vs. 0.170 ± 0.205 for AC-based indices) and a steeper increase before death. Two variance-based EWSs yielded HR95 > 9 (HR95 standing for a scale-invariant metric of hazard ratio), but combining them did not improve the area under the receiver-operating curve (AUC) much compared to using them alone (AUC = 0.798 vs. 0.796 and 0.791). Nevertheless, the AUC reached 0.825 when combining 13 indices. While some indicators did not perform overly well alone, their addition to the best performing EWSs increased the predictive power, suggesting that indices combination captures a broader range of dynamic changes occurring within the system. It is unclear whether this added benefit reflects measurement error of a unified phenomenon or heterogeneity in the nature of signals preceding critical transitions. Finally, the modest predictive performance and weak correlations among some indices call into question their validity, at least in this context.

Understanding change in benthic marine systems

BACKGROUND

The unprecedented influence of human activities on natural ecosystems in the 21st century has resulted in increasingly frequent large-scale changes in ecological communities. This has heightened interest in understanding such changes and effective means to manage them. Accurate interpretation of state changes is challenging because of difficulties translating theory to empirical study, and most theory emphasizes systems near equilibrium, which may not be relevant in rapidly changing environments.

SCOPE

We review concepts of long-transient stages and phase shifts between stable community states, both smooth, continuous and discontinuous shifts, and the relationships among them. Three principal challenges emerge when applying these concepts. The first is how to interpret observed change in communities - distinguishing multiple stable states from long transients, or reversible shifts in the phase portrait of single attractor systems. The second is how to quantify the magnitudes of three sources of variability that cause switches between community states: (1) 'noise' in species' abundances, (2) 'wiggle' in system parameters and (3) trends in parameters that affect the topography of the basin of attraction. The third challenge is how variability of the system shapes evidence used to interpret community changes. We outline a novel approach using critical length scales to potentially address these challenges. These concepts are highlighted by a review of recent examples involving macroalgae as key players in marine benthic ecosystems.

CONCLUSIONS

Real-world examples show three or more stable configurations of ecological communities may exist for a given set of parameters, and transient stages may persist for long periods necessitating their respective consideration. The characteristic length scale (CLS) is a useful metric that uniquely identifies a community 'basin of attraction', enabling phase shifts to be distinguished from long transients. Variabilities of CLSs and time series data may likewise provide proactive management measures to mitigate phase shifts and loss of ecosystem services. Continued challenges remain in distinguishing continuous from discontinuous phase shifts because their respective dynamics lack unique signatures.

Landscape quantifies the intermediate state and transition dynamics in ecological networks

Understanding the ecological mechanisms associated with the collapse and restoration is especially critical in promoting harmonious coexistence between humans and nature. So far, it remains challenging to elucidate the mechanisms of stochastic dynamical transitions for ecological systems. Using an example of plant-pollinator network, we quantified the energy landscape of ecological system. The landscape displays multiple attractors characterizing the high, low and intermediate abundance stable states. Interestingly, we detected the intermediate states under pollinator decline, and demonstrated the indispensable role of the intermediate state in state transitions. From the landscape, we define the barrier height (BH) as a global quantity to evaluate the transition feasibility. We propose that the BH can serve as a new early-warning signal (EWS) for upcoming catastrophic breakdown, which provides an earlier and more accurate warning signal than traditional metrics based on time series. Our results promote developing better management strategies to achieve environmental sustainability.

The collapse and re-establishment of stability regulate the gradual transition of bacterial communities from macrophytes- to phytoplankton-dominated types in a large eutrophic lake

Eutrophic lakes often exhibit two alternative types: macrophytes-dominated (MD) and phytoplankton-dominated (PD). However, the nature of bacterial community types that whether the transition from the MD to the PD types occurs in a gradual or abrupt manner remains hotly debated. Further, the theoretical recognition that stability regulates the transition of bacterial community types remains qualitative. To address these issues, we divided the transition of bacterial communities along a trophic gradient into 12 successional stages, ranging from the MD to the PD types. Results showed that 12 states were clustered into three distinct regimes: MD type, intermediate transitional type and PD type. Bacterial communities were not different between consecutive stages, suggesting that the transition of alternative types occurs in a continuous gradient. At the same time, the stability of bacterial communities was significantly lower in the intermediate type than in the MD or PD types, highlighting that the collapse and re-establishment of community stability regulate the transition. Further, our results showed that the high complexity of taxon interactions and strong stochastic processes disrupt the stability. Ultimately, this study enables deeper insights into understanding the alternative types of microbial communities in the view of community stability.

Systematic analysis and optimization of early warning signals for critical transitions using distribution data

Abrupt shifts between alternative regimes occur in complex systems, from cell regulation to brain functions to ecosystems. Several model-free early warning signals (EWS) have been proposed to detect impending transitions, but failure or poor performance in some systems have called for better investigation of their generic applicability. Notably, there are still ongoing debates whether such signals can be successfully extracted from data in particular from biological experiments. In this work, we systematically investigate properties and performance of dynamical EWS in different deteriorating conditions, and we propose an optimized combination to trigger warnings as early as possible, eventually verified on experimental data from microbiological populations. Our results explain discrepancies observed in the literature between warning signs extracted from simulated models and from real data, provide guidance for EWS selection based on desired systems and suggest an optimized composite indicator to alert for impending critical transitions using distribution data.

A predictive timeline of wildlife population collapse

Contemporary rates of biodiversity decline emphasize the need for reliable ecological forecasting, but current methods vary in their ability to predict the declines of real-world populations. Acknowledging that stressor effects start at the individual level, and that it is the sum of these individual-level effects that drives populations to collapse, shifts the focus of predictive ecology away from using predominantly abundance data. Doing so opens new opportunities to develop predictive frameworks that utilize increasingly available multi-dimensional data, which have previously been overlooked for ecological forecasting. Here, we propose that stressed populations will exhibit a predictable sequence of observable changes through time: changes in individuals' behaviour will occur as the first sign of increasing stress, followed by changes in fitness-related morphological traits, shifts in the dynamics (for example, birth rates) of populations and finally abundance declines. We discuss how monitoring the sequential appearance of these signals may allow us to discern whether a population is increasingly at risk of collapse, or is adapting in the face of environmental change, providing a conceptual framework to develop new forecasting methods that combine multi-dimensional (for example, behaviour, morphology, life history and abundance) data.

Alternative stable state and its evaluation in wetland reconstruction based on landscape design

An alternative stable state is closely related to the health and sustainable development of ecosystems; however, knowledge of the alternative stable state and its quantitative evaluation in wetland reconstruction remains incomplete. In this study, we used landscape design to reconstruct an optimized ecological polder wetland and a lake wetland in the Yunmeng Marsh area, China, and the alternative stable states of the two wetland ecosystems were assessed from an ecosystem perspective via emergy/eco-exergy and fractal dimensions. The emergy densities for the optimized ecological polder wetland and the lake wetland were 2.35E+13 sej yr^-1 m^-3 and 2.18E+13 sej m^-3, and the emergy sustainability index (ESI) values were 216.57 and 193.31, respectively, indicating that the reconstructed wetland ecosystems were dominated by renewable energy flows and were highly sustainable. The eco-exergy density and emergy/eco-exergy ratio results showed that natural selection self-organized the reconstructed wetland ecosystems to tolerate environmental stresses and changes. In addition, the fractal dimensions of the morphology and contour of the polder wetland, which reflect the space occupation capacity of geometric and physical constraints in the wetland, were 1.57 and 1.75, and those of the lake wetland were 1.03 and 1.47, respectively. The synthetic evaluation results showed that the alternative stable states of both the optimized ecological polder wetland ecosystem and the lake wetland ecosystem were ecofriendly modes of wetland reconstruction, which can be implemented together to create a "lake-polder" ecosystem. Our study on the alternative stable states of wetland ecosystems is helpful for exploring the synergistic symbiosis between traditional culture and the ecological environment in China and other wetland-rich regions and countries with severe disturbances.

Effects of diversity on thermal niche variation in bird communities under climate change

Climate change alters ecological communities by affecting individual species and interactions between species. However, the impacts of climate change may be buffered by community diversity: diverse communities may be more resistant to climate-driven perturbations than simple communities. Here, we assess how diversity influences long-term thermal niche variation in communities under climate change. We use 50-year continental-scale data on bird communities during breeding and non-breeding seasons to quantify the communities' thermal variability. Thermal variability is measured as the temporal change in the community's average thermal niche and it indicates community's response to climate change. Then, we study how the thermal variability varies as a function of taxonomic, functional, and evolutionary diversity using linear models. We find that communities with low thermal niche variation have higher functional diversity, with this pattern being measurable in the non-breeding but not in the breeding season. Given the expected increase in seasonal variation in the future climate, the differences in bird communities' thermal variability between breeding and non-breeding seasons may grow wider. Importantly, our results suggest that functionally diverse wildlife communities can mitigate effects of climate change by hindering changes in thermal niche variability, which underscores the importance of addressing the climate and biodiversity crises together.

Community structure determines the predictability of population collapse

Early warning signals (EWS) are phenomenological tools that have been proposed as predictors of the collapse of biological systems. Although a growing body of work has shown the utility of EWS based on either statistics derived from abundance data or shifts in phenotypic traits such as body size, so far this work has largely focused on single species populations.

However, to predict reliably the future state of ecological systems, which inherently could consist of multiple species, understanding how reliable such signals are in a community context is critical.

Here, reconciling quantitative trait evolution and Lotka–Volterra equations, which allow us to track both abundance and mean traits, we simulate the collapse of populations embedded in mutualistic and multi‐trophic predator–prey communities. Using these simulations and warning signals derived from both population‐ and community‐level data, we showed the utility of abundance‐based EWS, as well as metrics derived from stability‐landscape theory (e.g. width and depth of the basin of attraction), were fundamentally linked. Thus, the depth and width of such stability‐landscape curves could be used to identify which species should exhibit the strongest EWS of collapse.

The probability a species displays both trait and abundance‐based EWS was dependent on its position in a community, with some species able to act as indicator species. In addition, our results also demonstrated that in general trait‐based EWS were less reliable in comparison with abundance‐based EWS in forecasting species collapses in our simulated communities. Furthermore, community‐level abundance‐based EWS were fairly reliable in comparison with their species‐level counterparts in forecasting species‐level collapses.

Our study suggests a holistic framework that combines abundance‐based EWS and metrics derived from stability‐landscape theory that may help in forecasting species loss in a community context.

Spatiotemporal variability in Swedish lake ecosystems

Studying ecosystem dynamics is critical to monitoring and managing linked systems of humans and nature. Due to the growth of tools and techniques for collecting data, information on the condition of these systems is more widely available. While there are a variety of approaches for mining and assessing data, there is a need for methods to detect latent characteristics in ecosystems linked to temporal and spatial patterns of change. Resilience-based approaches have been effective at not only identifying environmental change but also providing warning in advance of critical transitions in social-ecological systems (SES). In this study, we examine the usefulness of one such method, Fisher Information (FI) for spatiotemporal analysis. FI is used to assess patterns in data and has been established as an effective tool for capturing complex system dynamics to include regimes and regime shifts. We employed FI to assess the biophysical condition of eighty-five Swedish lakes from 1996–2018. Results showed that FI captured spatiotemporal changes in the Swedish lakes and identified distinct spatial patterns above and below the Limes Norrlandicus, a hard ecotone boundary which separates northern and southern ecoregions in Sweden. Further, it revealed that spatial variance changed approaching this boundary. Our results demonstrate the utility of this resilience-based approach for spatiotemporal and spatial regimes analyses linked to monitoring and managing critical watersheds and waterbodies impacted by accelerating environmental change.

Photo-acclimatory thresholds anticipate sudden shifts in seagrass ecosystem state under reduced light conditions

Seagrass ecosystems usually respond in a nonlinear fashion to increasing pressures and environmental changes. Feedback mechanisms operating at the ecosystem level and involving multiple interactions among the seagrass meadow, its associated community and the physical environment are known to play a major role in such nonlinear responses. Phenotypic plasticity may also be important for buffering these ecological thresholds (i.e., regime shifts) as many physiological processes show nonlinear responses to gradual environmental changes, conferring the appearance of resistance before the effects at the organism and population levels are visible. However, the potential involvement of plant plasticity in driving catastrophic shifts in seagrass ecosystems has not yet been assessed. In this study, we conducted a manipulative 6-month light-gradient experiment in the field to capture nonlinearities of the physiological and population responses of the seagrass Cymodocea nodosa to gradual light reduction. The aim was to explore if and how the photo-acclimatory responses of shaded plants are translated to the population level and, hence, to the ecosystem level. Results showed that the seagrass population was rather stable under increasing shading levels through the activation of multilevel photo-acclimative responses, which are initiated with light reduction and modulated in proportion to shading intensity. The activation of photo-physiological and metabolic compensatory responses allowed shaded plants to sustain nearly constant plant productivity (metabolic carbon balance) along a range of shading levels before losing linearity and starting to decline. The species then activated plant- and meadow-scale photo-acclimative responses and drew on its energy reserves (rhizome carbohydrates) to confer additional population resilience. However, when the integration of all these buffering mechanisms failed to counterbalance the effects of extreme light limitation, the population collapsed, giving place to a phase shift from vegetated to bare sediments with catastrophic ecosystem outcomes. Our findings evidence that ecological thresholds in seagrass ecosystems under light limitation can be explained by the role of species' compensatory responses in modulating population-level responses. The thresholds of these plastic responses anticipate the sudden loss of seagrass meadows with the potential to be used as early warning indicators signalling the imminent collapse of the ecosystem, which is of great value for the real-world management of seagrass ecosystems.

Machine learning methods trained on simple models can predict critical transitions in complex natural systems

Forecasting sudden changes in complex systems is a critical but challenging task, with previously developed methods varying widely in their reliability. Here we develop a novel detection method, using simple theoretical models to train a deep neural network to detect critical transitions-the Early Warning Signal Network (EWSNet). We then demonstrate that this network, trained on simulated data, can reliably predict observed real-world transitions in systems ranging from rapid climatic change to the collapse of ecological populations. Importantly, our model appears to capture latent properties in time series missed by previous warning signals approaches, allowing us to not only detect if a transition is approaching, but critically whether the collapse will be catastrophic or non-catastrophic. These novel properties mean EWSNet has the potential to serve as an indicator of transitions across a broad spectrum of complex systems, without requiring information on the structure of the system being monitored. Our work highlights the practicality of deep learning for addressing further questions pertaining to ecosystem collapse and has much broader management implications.

The coupled socio-ecohydrological evolution of river systems: Towards an integrative perspective of river systems in the 21st century

River systems have undergone a massive transformation since the Anthropocene. The natural properties of river systems have been drastically altered and reshaped, limiting the use of management frameworks, their scientific knowledge base and their ability to provide adequate solutions for current problems and those of the future, such as climate change, biodiversity crisis and increased demands for water resources. To address these challenges, a socioecologically driven research agenda for river systems that complements current approaches is needed and proposed. The implementation of the concepts of social metabolism and the colonisation of natural systems into existing concepts can provide a new basis to analyse the coevolutionary coupling of social systems with ecological and hydrological (i.e., 'socio-ecohydrological') systems within rivers. To operationalize this research agenda, we highlight four initial core topics defined as research clusters (RCs) to address specific system properties in an integrative manner. The colonisation of natural systems by social systems is seen as a significant driver of the transformation processes in river systems. These transformation processes are influenced by connectivity (RC 1), which primarily addresses biophysical aspects and governance (RC 2), which focuses on the changes in social systems. The metabolism (RC 3) and vulnerability (RC 4) of the social and natural systems are significant aspects of the coupling of social systems and ecohydrological systems with investments, energy, resources, services and associated risks and impacts. This socio-ecohydrological research agenda complements other recent approaches, such as 'socio-ecological', 'socio-hydrological' or 'socio-geomorphological' systems, by focusing on the coupling of social systems with natural systems in rivers and thus, by viewing the socioeconomic features of river systems as being just as important as their natural characteristics. The proposed research agenda builds on interdisciplinarity and transdisciplinarity and requires the implementation of such programmes into the education of a new generation of river system scientists, managers and engineers who are aware of the transformation processes and the coupling between systems.

A Science Agenda to Inform Natural Resource Management Decisions in an Era of Ecological Transformation

Earth is experiencing widespread ecological transformation in terrestrial, freshwater, and marine ecosystems that is attributable to directional environmental changes, especially intensifying climate change. To better steward ecosystems facing unprecedented and lasting change, a new management paradigm is forming, supported by a decision-oriented framework that presents three distinct management choices: resist, accept, or direct the ecological trajectory. To make these choices strategically, managers seek to understand the nature of the transformation that could occur if change is accepted while identifying opportunities to intervene to resist or direct change. In this article, we seek to inspire a research agenda for transformation science that is focused on ecological and social science and based on five central questions that align with the resist–accept–direct (RAD) framework. Development of transformation science is needed to apply the RAD framework and support natural resource management and conservation on our rapidly changing planet.

Phase transitions in biology: from bird flocks to population dynamics

Phase transitions are an important and extensively studied concept in physics. The insights derived from understanding phase transitions in physics have recently and successfully been applied to a number of different phenomena in biological systems. Here, we provide a brief review of phase transitions and their role in explaining biological processes ranging from collective behaviour in animal flocks to neuronal firing. We also highlight a new and exciting area where phase transition theory is particularly applicable: population collapse and extinction. We discuss how phase transition theory can give insight into a range of extinction events such as population decline due to climate change or microbial responses to stressors such as antibiotic treatment.

Scientific foundations for an ecosystem goal, milestones and indicators for the post-2020 global biodiversity framework

Despite substantial conservation efforts, the loss of ecosystems continues globally, along with related declines in species and nature's contributions to people. An effective ecosystem goal, supported by clear milestones, targets and indicators, is urgently needed for the post-2020 global biodiversity framework and beyond to support biodiversity conservation, the UN Sustainable Development Goals and efforts to abate climate change. Here, we describe the scientific foundations for an ecosystem goal and milestones, founded on a theory of change, and review available indicators to measure progress. An ecosystem goal should include three core components: area, integrity and risk of collapse. Targets-the actions that are necessary for the goals to be met-should address the pathways to ecosystem loss and recovery, including safeguarding remnants of threatened ecosystems, restoring their area and integrity to reduce risk of collapse and retaining intact areas. Multiple indicators are needed to capture the different dimensions of ecosystem area, integrity and risk of collapse across all ecosystem types, and should be selected for their fitness for purpose and relevance to goal components. Science-based goals, supported by well-formulated action targets and fit-for-purpose indicators, will provide the best foundation for reversing biodiversity loss and sustaining human well-being.

The futility of long-term predictions in bipolar disorder: mood fluctuations are the result of deterministic chaotic processes

BACKGROUND

Understanding the underlying architecture of mood regulation in bipolar disorder (BD) is important, as we are starting to conceptualize BD as a more complex disorder than one of recurring manic or depressive episodes. Nonlinear techniques are employed to understand and model the behavior of complex systems. Our aim was to assess the underlying nonlinear properties that account for mood and energy fluctuations in patients with BD; and to compare whether these processes were different in healthy controls (HC) and unaffected first-degree relatives (FDR). We used three different nonlinear techniques: Lyapunov exponent, detrended fluctuation analysis and fractal dimension to assess the underlying behavior of mood and energy fluctuations in all groups; and subsequently to assess whether these arise from different processes in each of these groups.

RESULTS

There was a positive, short-term autocorrelation for both mood and energy series in all three groups. In the mood series, the largest Lyapunov exponent was found in HC (1.84), compared to BD (1.63) and FDR (1.71) groups [F (2, 87) = 8.42, p < 0.005]. A post-hoc Tukey test showed that Lyapunov exponent in HC was significantly higher than both the BD (p = 0.003) and FDR groups (p = 0.03). Similarly, in the energy series, the largest Lyapunov exponent was found in HC (1.85), compared to BD (1.76) and FDR (1.67) [F (2, 87) = 11.02; p < 0.005]. There were no significant differences between groups for the detrended fluctuation analysis or fractal dimension.

CONCLUSIONS

The underlying nature of mood variability is in keeping with that of a chaotic system, which means that fluctuations are generated by deterministic nonlinear process(es) in HC, BD, and FDR. The value of this complex modeling lies in analyzing the nature of the processes involved in mood regulation. It also suggests that the window for episode prediction in BD will be inevitably short.

Probabilistic early warning signals

Ecological communities and other complex systems can undergo abrupt and long-lasting reorganization, a regime shift, when deterministic or stochastic factors bring them to the vicinity of a tipping point between alternative states. Such changes can be large and often arise unexpectedly. However, theoretical and experimental analyses have shown that changes in correlation structure, variance, and other standard indicators of biomass, abundance, or other descriptive variables are often observed prior to a state shift, providing early warnings of an anticipated transition. Natural systems manifest unknown mixtures of ecological and environmental processes, hampered by noise and limited observations. As data quality often cannot be improved, it is important to choose the best modeling tools available for the analysis.We investigate three autoregressive models and analyze their theoretical differences and practical performance. We formulate a novel probabilistic method for early warning signal detection and demonstrate performance improvements compared to nonprobabilistic alternatives based on simulation and publicly available experimental time series.The probabilistic formulation provides a novel approach to early warning signal detection and analysis, with enhanced robustness and treatment of uncertainties. In real experimental time series, the new probabilistic method produces results that are consistent with previously reported findings.Robustness to uncertainties is instrumental in the common scenario where mechanistic understanding of the complex system dynamics is not available. The probabilistic approach provides a new family of robust methods for early warning signal detection that can be naturally extended to incorporate variable modeling assumptions and prior knowledge.

Tipping Cascades in a Multi-patch System with Noise and Spatial Coupling

Forecasting tipping points in spatially extended systems is a key area of interest to ecologists. A slowly declining spatially distributed population is an important example of an ecological system that could exhibit a cascade of tipping points. Here, we develop a spatial two-patch model with environmental stochasticity that is slowly forced through population collapse, in the presence of changing environmental conditions. We begin with a basic spatial model, then introduce a fast-slow version of the model using geometric singular perturbation theory, followed by the inclusion of stochasticity. Using the spectral density of the fluctuating subpopulation in each patch, we derive analytic expressions for candidate indicators of population extinction and evaluate their performance through a simulation study. We find that coupling and spatial heterogeneity decrease the magnitude of the proposed indicators in coupled populations relative to isolated populations. Moreover, the degree of coupling dictates the trends in summary statistics. We conclude that this theory may be applied to other contexts, including the control of invasive species.

Density dependence can obscure nonlethal effects of disturbance on life history of medium-sized cetaceans

Nonlethal disturbance of animals can cause behavioral and physiological changes that affect individual health status and vital rates, with potential consequences at the population level. Predicting these population effects remains a major challenge in ecology and conservation. Monitoring fitness-related traits may improve detection of upcoming population changes, but the extent to which individual traits are reliable indicators of disturbance exposure is not well understood, especially for populations regulated by density dependence. Here we study how density dependence affects a population’s response to disturbance and modifies the disturbance effects on individual health and vital rates. We extend an energy budget model for a medium-sized cetacean (the long-finned pilot whale Globicephala melas) to an individual-based population model in which whales feed on a self-replenishing prey base and disturbance leads to cessation of feeding. In this coupled predator-prey system, the whale population is regulated through prey depletion and the onset of yearly repeating disturbances on the whale population at carrying capacity decreased population density and increased prey availability due to reduced top-down control. In populations faced with multiple days of continuous disturbance each year, female whales that were lactating their first calf experienced increased mortality due to depletion of energy stores. However, increased prey availability led to compensatory effects and resulted in a subsequent improvement of mean female body condition, mean age at first reproduction and higher age-specific reproductive output. These results indicate that prey-mediated density dependence can mask negative effects of disturbance on fitness-related traits and vital rates, a result with implications for the monitoring and management of marine mammal populations.

When and Where We Can Expect to See Early Warning Signals in Multispecies Systems Approaching Tipping Points: Insights from Theory

AbstractEarly warning signals (EWSs) have the potential to predict tipping points where catastrophic changes occur in ecological systems. However, EWSs are plagued by false negatives, leading to undetected catastrophes. One reason may be because EWSs do not occur equally for all species in a system, so whether and how strongly EWSs are detected depends on which species is being observed. Here, we illustrate how the strength of EWSs is determined by each species' relationship to properties of the noise, the system's response to that noise, and the occurrence of critical slowing down (the dynamical phenomenon that gives rise to EWSs). Using these relationships, we present general rules for maximizing EWS detection in ecological communities. We find that for two-species competitive and mutualistic systems, one should generally monitor the species experiencing smaller intraspecific effects to maximize EWS performance, while in consumer-resource systems, one should monitor the species imposing the smaller interspecific effects. These guidelines appear to hold for at least some larger communities as well. We close by extending the theoretical basis for our rules to systems with any number of species and more complex forms of noise. Our findings provide important guidance on how to monitor systems for EWSs to maximize detection of tipping points.

Early warning indicators of population collapse in a seasonal environment

Recent studies have demonstrated that generic statistical signals derived from time series of population abundance and fitness-related traits of individuals can provide reliable indicators of impending shifts in population dynamics. However, how the seasonal timing of environmental stressors influences these early warning indicators is not well understood. The goal of this study was to experimentally assess whether the timing of stressors influences the production, detection and sensitivity of abundance- and trait-based early warning indicators derived from declining populations. In a multi-generation, season-specific habitat loss experiment, we exposed replicate populations of Drosophila melanogaster to one of two rates of chronic habitat loss (10% or 20% per generation) in either the breeding or the non-breeding period. We counted population abundance at the beginning of each season, and measured body mass and activity levels in a sample of individuals at the end of each generation. When habitat was lost during the breeding period, declining populations produced signals consistent with those documented in previous studies. Inclusion of trait-based indicators generally improved the detection of impending population collapse. However, when habitat was lost during the non-breeding period, the predictive capacity of these indicators was comparatively diminished. Our results have important implications for interpreting signals in the wild because they suggest that the production and detection of early warning indicators depends on the season in which stressors occur, and that this is likely related to the capacity of populations to respond numerically the following season.

Corridor quality affects net movement, size of dispersers, and population growth in experimental microcosms

Corridors are expected to increase species dispersal in fragmented habitats. However, it remains unclear how the quality of corridors influences the dispersal process, and how it interacts with corridor length and width. Here we investigate these factors using a small-scale laboratory system where we track the dispersal of the model organism Collembola Folsomia candida. Using this system, we study the effects of corridor length, width, and quality on the probability of dispersal, net movement, body size of dispersers, and the rate of change in population size after colonization. We show that corridor quality positively affected dispersal probability, net movement, and the rate of change in population size in colonised patches. Moreover, corridor quality significantly affected the size of dispersers, with only larger individuals dispersing through poor quality corridors. The length and width of corridors affected both the rate at which populations increased in colonised patches and the net number of individuals which dispersed, suggesting that these physical properties may be important in maintaining the flow of individuals in space. Our results thus suggest that corridor quality can have an important role in determining not only the probability of dispersal occurs but also the phenotypes of the individuals which disperse, with concomitant effects on the net movement of individuals and the rate of change in population size in the colonised patches.

Cumulative stressors reduce the self-regulating capacity of coastal ecosystems

Marine ecosystems are prone to tipping points, particularly in coastal zones where dramatic changes are associated with interactions between cumulative stressors (e.g., shellfish harvesting, eutrophication and sediment inputs) and ecosystem functions. A common feature of many degraded estuaries is elevated turbidity that reduces incident light to the seafloor, resulting from multiple factors including changes in sediment loading, sea-level rise and increased water column algal biomass. To determine whether cumulative effects of elevated turbidity may result in marked changes in the interactions between ecosystem components driving nutrient processing, we conducted a large-scale experiment manipulating sediment nitrogen concentrations in 15 estuaries across a national-scale gradient in incident light at the seafloor. We identified a threshold in incident light that was related to distinct changes in the ecosystem interaction networks (EIN) that drive nutrient processing. Above this threshold, network connectivity was high with clear mechanistic links to denitrification and the role of large shellfish in nitrogen processing. The EIN analyses revealed interacting stressors resulting in a decoupling of ecosystem processes in turbid estuaries with a lower capacity to denitrify and process nitrogen. This suggests that, as turbidity increases with sediment load, coastal areas can be more vulnerable to eutrophication. The identified interactions between light, nutrient processing and the abundance of large shellfish emphasizes the importance of actions that seek to manage multiple stressors and conserve or enhance shellfish abundance, rather than actions focusing on limiting a single stressor.

Disentangling the dynamical underpinnings of differences in SARS-CoV-2 pathology using within-host ecological models

Health outcomes following infection with Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) are remarkably variable. The way the virus spreads inside hosts, and how this spread interacts with host immunity and physiology, is likely to determine variation in health outcomes. Decades of data and dynamical analyses of how other viruses spread and interact with host cells could shed light on SARS-CoV-2 within-host trajectories. We review how common axes of variation in within-host dynamics and emergent pathology (such as age and sex) might be combined with ecological principles to understand the case of SARS-CoV-2. We highlight pitfalls in application of existing theoretical frameworks relevant to the complexity of the within-host context and frame the discussion in terms of growing knowledge of the biology of SARS-CoV-2. Viewing health outcomes for SARS-CoV-2 through the lens of ecological models underscores the value of repeated measures on individuals, especially since many lines of evidence suggest important contingence on trajectory.

Detecting and distinguishing tipping points using spectral early warning signals

Theory and observation tell us that many complex systems exhibit tipping points—thresholds involving an abrupt and irreversible transition to a contrasting dynamical regime. Such events are commonly referred to as critical transitions. Current research seeks to develop early warning signals (EWS) of critical transitions that could help prevent undesirable events such as ecosystem collapse. However, conventional EWS do not indicate the type of transition, since they are based on the generic phenomena of critical slowing down. For instance, they may fail to distinguish the onset of oscillations (e.g. Hopf bifurcation) from a transition to a distant attractor (e.g. Fold bifurcation). Moreover, conventional EWS are less reliable in systems with density-dependent noise. Other EWS based on the power spectrum (spectral EWS) have been proposed, but they rely upon spectral reddening, which does not occur prior to critical transitions with an oscillatory component. Here, we use Ornstein–Uhlenbeck theory to derive analytic approximations for EWS prior to each type of local bifurcation, thereby creating new spectral EWS that provide greater sensitivity to transition proximity; higher robustness to density-dependent noise and bifurcation type; and clues to the type of approaching transition. We demonstrate the advantage of applying these spectral EWS in concert with conventional EWS using a population model, and show that they provide a characteristic signal prior to two different Hopf bifurcations in data from a predator–prey chemostat experiment. The ability to better infer and differentiate the nature of upcoming transitions in complex systems will help humanity manage critical transitions in the Anthropocene Era.

Using paleo-archives to safeguard biodiversity under climate change

Strategies for 21st-century environmental management and conservation under global change require a strong understanding of the biological mechanisms that mediate responses to climate- and human-driven change to successfully mitigate range contractions, extinctions, and the degradation of ecosystem services. Biodiversity responses to past rapid warming events can be followed in situ and over extended periods, using cross-disciplinary approaches that provide cost-effective and scalable information for species' conservation and the maintenance of resilient ecosystems in many bioregions. Beyond the intrinsic knowledge gain such integrative research will increasingly provide the context, tools, and relevant case studies to assist in mitigating climate-driven biodiversity losses in the 21st century and beyond.

The Ecosystem Resilience Concept Applied to Hydrogeological Systems: A General Approach

We have witnessed the great changes that hydrogeological systems are facing in the last decades: rivers that have dried up; wetlands that have disappeared, leaving their buckets converted into farmland; and aquifers that have been intensively exploited for years, among others. Humans have caused the most part of these results that can be worsened by climate change, with delayed effects on groundwater quantity and quality. The consequences are negatively impacting ecosystems and dependent societies. The concept of resilience has not been extensively used in the hydrogeological research, and it can be a very useful concept that can improve the understanding and management of these systems. The aim of this work is to briefly discuss the role of resilience in the context of freshwater systems affected by either climate or anthropic actions as a way to increase our understanding of how anticipating negative changes (transitions) may contribute to improving the management of the system and preserving the services that it provides. First, the article presents the basic concepts applied to hydrogeological systems from the ecosystem’s resilience approach. Second, the factors controlling for hydrogeological systems’ responses to different impacts are commented upon. Third, a case study is analyzed and discussed. Finally, the useful implications of the concept are discussed.

Manipulating the strength of organism-environment feedback increases nonlinearity and apparent hysteresis of ecosystem response to environmental change

Theory predicts that organism-environment feedbacks play a central role in how ecological communities respond to environmental change. Strong feedback causes greater nonlinearity between environmental change and ecosystem state, increases the likelihood of hysteresis in response to environmental change, and augments the possibility of alternative stable regimes. To illustrate these predictions and their dependence on a temporal scale, we simulated a minimal ecosystem model. To test the predictions, we manipulated the feedback strength between the metabolism and the dissolved oxygen concentration in an aquatic heterotrophic tri-trophic community in microecosystems. The manipulation consisted of five levels, ranging from low to high feedback strength by altering the oxygen diffusivity: free gas exchange between the microcosm atmosphere and the external air (metabolism not strongly affecting environmental oxygen), with the regular addition of 200, 100, or 50 ml of air and no gas exchange. To test for nonlinearity and hysteresis in response to environmental change, all microecosystems experienced a gradual temperature increase from 15 to 25°C and then back to 15°C. We regularly measured the dissolved oxygen concentration, total biomass, and species abundance. Nonlinearity and hysteresis were higher in treatments with stronger organism-environment feedbacks. There was no evidence that stronger feedback increased the number of observed ecosystem states. These empirical results are in broad agreement with the theory that stronger feedback increases nonlinearity and hysteresis. They therefore represent one of the first direct empirical tests of the importance of feedback strength. However, we discuss several limitations of the study, which weaken confidence in this interpretation. Research demonstrating the causal effects of feedback strength on ecosystem responses to environmental change should be placed at the core of efforts to plan for sustainable ecosystems.

Towards a Comparative Framework of Demographic Resilience

In the current global biodiversity crisis, the development of tools to define, quantify, compare, and predict resilience is essential for understanding the responses of species to global change. However, disparate interpretations of resilience have hampered the development of a common currency to quantify and compare resilience across natural systems. Most resilience frameworks focus on upper levels of biological organization, especially ecosystems or communities, which complicates measurements of resilience using empirical data. Surprisingly, there is no quantifiable definition of resilience at the demographic level. We introduce a framework of demographic resilience that draws on existing concepts from community and population ecology, as well as an accompanying set of metrics that are comparable across species.

Modifying connectivity to promote state change reversal: the importance of geomorphic context and plant-soil feedbacks

Alternative states maintained by feedbacks are notoriously difficult, if not impossible, to reverse. Although positive interactions that modify soil conditions may have the greatest potential to alter self-reinforcing feedbacks, the conditions leading to these state change reversals have not been resolved. In a 9-yr study, we modified horizontal connectivity of resources by wind or water on different geomorphic surfaces in an attempt to alter plant-soil feedbacks and shift woody-plant-dominated states back toward perennial grass dominance. Modifying connectivity resulted in an increase in litter cover regardless of the vector of transport (wind, water) followed by an increase in perennial grass cover 2 yr later. Modifying connectivity was most effective on sandy soils where wind is the dominant vector, and least effective on gravelly soils on stable surfaces with low sediment movement by water. We found that grass cover was related to precipitation in the first 5 yr of our study, and plant-soil feedbacks developed following 6 yr of modified connectivity to overwhelm effects of precipitation on sandy, wind-blown soils. These feedbacks persisted through time under variable annual rainfall. On alluvial soils, either plant-soil feedbacks developed after 7 yr that were not persistent (active soils) or did not develop (stable soils). This novel approach has application to drylands globally where desertified lands have suffered losses in ecosystem services, and to other ecosystems where connectivity-mediated feedbacks modified at fine scales can be expected to impact plant recovery and state change reversals at larger scales, in particular for wind-impacted sites.

Effect of time series length and resolution on abundance- and trait-based early warning signals of population declines

Natural populations are increasingly threatened with collapse at the hands of anthropogenic effects. Predicting population collapse with the help of generic early warning signals (EWS) may provide a prospective tool for identifying species or populations at highest risk. However, pattern-to-process methods such as EWS have a multitude of challenges to overcome to be useful, including the low signal-to-noise ratio of ecological systems and the need for high quality time series data. The inclusion of trait dynamics with EWS has been proposed as a more robust tool to predict population collapse. However, the length and resolution of available time series are highly variable from one system to another, especially when generation time is considered. As yet, it remains unknown how this variability with regards to generation time will alter the efficacy of EWS. Here we take both a simulation- and experimental-based approach to assess the impacts of relative time series length and resolution on the forecasting ability of EWS. We show that EWS' performance decreases with decreasing time-series length. However, there was no evident decrease in EWS performance as resolution decreased. Our simulations suggest a relative time series length between 10 and five generations as a minimum requirement for accurate forecasting by abundance-based EWS. However, when trait information is included alongside abundance-based EWS, we find positive signals at lengths one-half of what was required without them. We suggest that, in systems where specific traits are known to affect demography, trait data should be monitored and included alongside abundance data to improve forecasting reliability.

Period doubling as an indicator for ecosystem sensitivity to climate extremes

The predictions for a warmer and drier climate and for increased likelihood of climate extremes raise high concerns about the possible collapse of dryland ecosystems, and about the formation of new drylands where native species are less tolerant to water stress. Using a dryland-vegetation model for plant species that display different tradeoffs between fast growth and tolerance to droughts, we find that ecosystems subjected to strong seasonal variability, typical for drylands, exhibit a temporal period-doubling route to chaos that results in early collapse to bare soil. We further find that fast-growing plants go through period doubling sooner and span wider chaotic ranges than stress-tolerant plants. We propose the detection of period-doubling signatures in power spectra as early indicators of ecosystem collapse that outperform existing indicators in their ability to warn against climate extremes and capture the heightened vulnerability of newly-formed drylands. The proposed indicator is expected to apply to other types of ecosystems, such as consumer–resource and predator–prey systems. We conclude by delineating the conditions ecosystems should meet in order for the proposed indicator to apply.

Research questions to facilitate the future development of European long-term ecosystem research infrastructures: A horizon scanning exercise

Distributed environmental research infrastructures are important to support assessments of the effects of global change on landscapes, ecosystems and society. These infrastructures need to provide continuity to address long-term change, yet be flexible enough to respond to rapid societal and technological developments that modify research priorities. We used a horizon scanning exercise to identify and prioritize emerging research questions for the future development of ecosystem and socio-ecological research infrastructures in Europe. Twenty research questions covered topics related to (i) ecosystem structures and processes, (ii) the impacts of anthropogenic drivers on ecosystems, (iii) ecosystem services and socio-ecological systems and (iv), methods and research infrastructures. Several key priorities for the development of research infrastructures emerged. Addressing complex environmental issues requires the adoption of a whole-system approach, achieved through integration of biotic, abiotic and socio-economic measurements. Interoperability among different research infrastructures needs to be improved by developing standard measurements, harmonizing methods, and establishing capacities and tools for data integration, processing, storage and analysis. Future research infrastructures should support a range of methodological approaches including observation, experiments and modelling. They should also have flexibility to respond to new requirements, for example by adjusting the spatio-temporal design of measurements. When new methods are introduced, compatibility with important long-term data series must be ensured. Finally, indicators, tools, and transdisciplinary approaches to identify, quantify and value ecosystem services across spatial scales and domains need to be advanced.

Simple signals indicate which period of the annual cycle drives declines in seasonal populations

For declining wild populations, a critical aspect of effective conservation is understanding when and where the causes of decline occur. The primary drivers of decline in migratory and seasonal populations can often be attributed to a specific period of the year. However, generic, broadly applicable indicators of these season-specific drivers of population decline remain elusive. We used a multi-generation experiment to investigate whether habitat loss in either the breeding or non-breeding period generated distinct signatures of population decline. When breeding habitat was reduced, population size remained relatively stable for several generations, before declining precipitously. When non-breeding habitat was reduced, between-season variation in population counts increased relative to control populations, and non-breeding population size declined steadily. Changes in seasonal vital rates and other indicators were predicted by the season in which habitat loss treatment occurred. Per capita reproductive output increased when non-breeding habitat was reduced and decreased with breeding habitat reduction, whereas per capita non-breeding survival showed the opposite trends. Our results reveal how simple signals inherent in counts and demographics of declining populations can indicate which period of the annual cycle is driving declines.

Eco-evolutionary processes underlying early warning signals of population declines

Environmental change can impact the stability of ecological systems and cause rapid declines in populations. Abundance-based early warning signals have been shown to precede such declines, but detection prior to wild population collapses has had limited success, leading to the development of warning signals based on shifts in distribution of fitness-related traits such as body size. The dynamics of population abundances and traits in response to external environmental perturbations are controlled by a range of underlying factors such as reproductive rate, genetic variation and plasticity. However, it remains unknown how such ecological and evolutionary factors affect the stability landscape of populations and the detectability of abundance and trait-based early warning signals. Here, we apply a trait-based demographic approach and investigate both trait and population dynamics in response to gradual and increasing changes in the environment. We explore a range of ecological and evolutionary constraints under which stability of a population may be affected. We show both analytically and with simulations that strength of abundance- and trait-based warning signals are affected by ecological and evolutionary factors. Finally, we show that combining trait- and abundance-based information improves our ability to predict population declines. Our study suggests that the inclusion of trait dynamic information alongside generic warning signals should provide more accurate forecasts of the future state of biological systems.

Complex System Approaches for Animal Health Surveillance

Many new and highly variable data are currently being produced by the many participants in farmed animal productions systems. These data hold the promise of new information with potential value for animal health surveillance. The current analytical paradigm for dealing with these new data is to implement syndromic surveillance systems, which focus mainly on univariate event detection methods applied to individual time series, with the goal of identifying epidemics in the population. This approach is relatively limited in the scope and not well-suited for extracting much of the additional information that is contained within these data. These approaches have value and should not be abandoned. However, an additional, new analytical paradigm will be needed if surveillance and disease control agencies wish to extract additional information from these data. We propose a more holistic analytical approach borrowed from complex system science that considers animal disease to be a product of the complex interactions between the many individuals, organizations and other factors that are involved in, or influence food production systems. We will discuss the characteristics of farmed animal food production systems that make them complex adaptive systems and propose practical applications of methods borrowed from complex system science to help animal health surveillance practitioners extract additional information from these new data.

Inferring critical thresholds of ecosystem transitions from spatial data

Ecosystems can undergo abrupt transitions between alternative stable states when the driver crosses a critical threshold. Dynamical systems theory shows that when ecosystems approach the point of loss of stability associated with these transitions, they take a long time to recover from perturbations, a phenomenon known as critical slowing down. This generic feature of dynamical systems can offer early warning signals of abrupt transitions. However, these signals are qualitative and cannot quantify the thresholds of drivers at which transition may occur. Here, we propose a method to estimate critical thresholds from spatial data. We show that two spatial metrics, spatial variance and autocorrelation of ecosystem state variable, computed along driver gradients can be used to estimate critical thresholds. First, we investigate cellular-automaton models of ecosystem dynamics that show a transition from a high-density state to a bare state. Our models show that critical thresholds can be estimated as the ecosystem state and the driver values at which spatial variance and spatial autocorrelation of the ecosystem state are maximum. Next, to demonstrate the application of the method, we choose remotely sensed vegetation data (Enhanced Vegetation Index, EVI) from regions in central Africa and northeast Australia that exhibit alternative states in woody cover. We draw transects (8 × 90 km) that span alternative stable states along rainfall gradients. Our analyses of spatial variance and autocorrelation of EVI along transects yield estimates of critical thresholds. These estimates match reasonably well with those obtained by an independent method that uses large-scale (250 × 200 km) spatial data sets. Given the generality of the principles that underlie our method, our method can be applied to a variety of ecosystems that exhibit alternative stable states.

Bifurcation or state tipping: assessing transition type in a model trophic cascade

Ecosystems can experience sudden regime shifts due to a variety of mechanisms. Two of the ways a system can cross a tipping point include when a perturbation to the system state is large enough to push the system beyond the basin of attraction of one stable state and into that of another (state tipping), and alternately, when slow changes to some underlying parameter lead to a fold bifurcation that annihilates one of the stable states. The first mechanism does not generate the phenomenon of critical slowing down (CSD), whereas the latter does generate CSD, which has been postulated as a way to detect early warning signs ahead of a sudden shift. Yet distinguishing between the two mechanisms (s-tipping and b-tipping) is not always as straightforward as it might seem. The distinction between "state" and "parameter" that may seem self-evident in mathematical equations depends fundamentally on ecological details in model formulation. This distinction is particularly relevant when considering high-dimensional models involving trophic webs of interacting species, which can only be reduced to a one-dimensional model of a tipping point under appropriate consideration of both the mathematics and biology involved. Here we illustrate that process of dimension reduction and distinguishing between s- and b-tipping for a highly influential trophic cascade model used to demonstrate tipping points and test CSD predictions in silico, and later, in a natural lake ecosystem. Our analysis resolves a previously unclear issue as to the nature of the tipping point involved.

Early warning signals of recovery in complex systems

Early warning signals (EWSs) offer the hope that patterns observed in data can predict the future states of ecological systems. While a large body of research identifies such signals prior to the collapse of populations, the prediction that such signals should also be present before a system’s recovery has thus far been overlooked. We assess whether EWSs are present prior to the recovery of overexploited marine systems using a trait-based ecological model and analysis of real-world fisheries data. We show that both abundance and trait-based signals are independently detectable prior to the recovery of stocks, but that combining these two signals provides the best predictions of recovery. This work suggests that the efficacy of conservation interventions aimed at restoring systems which have collapsed may be predicted prior to the recovery of the system, with direct relevance for conservation planning and policy.

While several studies have documented early warning signals of population collapse, the use of such signals as indicators of population recovery has not been investigated. Here the authors use models and empirical fisheries data to show that there are statistical indicators preceding recovery of cod populations.

When Do Shifts in Trait Dynamics Precede Population Declines?

Predicting population responses to environmental change is an ongoing challenge in ecology. Studies investigating the links between fitness-related phenotypic traits and demography have shown that trait dynamic responses to environmental change can sometimes precede population dynamic responses and thus can be used as an early warning signal. However, it is still unknown under which ecological and evolutionary circumstances shifts in fitness-related traits can precede population responses to environmental perturbation. Here, we take a trait-based demographic approach and investigate both trait and population dynamics in a density-regulated population in response to a gradual change in the environment. We explore the ecological and evolutionary constraints under which shifts in fitness-related traits precede a decline in population size. We show both analytically and with experimental data that under medium to slow rates of environmental change, shifts in a trait value can precede population decline. We further show the positive influence of environmental predictability, net reproductive rate, plasticity, and genetic variation on shifts in trait dynamics preceding potential population declines. These results still hold under nonconstant genetic variation and environmental stochasticity. Our study highlights ecological and evolutionary circumstances under which a fitness-related trait can be used as an early warning signal of an impending population decline.

An information theory-based approach to assessing spatial patterns in complex systems

Given the intensity and frequency of environmental change, the linked and cross-scale nature of social-ecological systems, and the proliferation of big data, methods that can help synthesize complex system behavior over a geographical area are of great value. Fisher information evaluates order in data and has been established as a robust and effective tool for capturing changes in system dynamics, including the detection of regimes and regime shifts. Methods developed to compute Fisher information can accommodate multivariate data of various types and requires no a priori decisions about system drivers, making it a unique and powerful tool. However, the approach has primarily been used to evaluate temporal patterns. In its sole application to spatial data, Fisher information successfully detected regimes in terrestrial and aquatic systems over transects. Although the selection of adjacently positioned sampling stations provided a natural means of ordering the data, such an approach limits the types of questions that can be answered in a spatial context. Here, we expand the approach to develop a method for more fully capturing spatial dynamics. Results reflect changes in the index that correspond with geographical patterns and demonstrate the utility of the method in uncovering hidden spatial trends in complex systems.